Mathematical Modeling in Finance with Stochastic Processes

38 CHAPTER 1. BACKGROUND IDEAS

Outside Readings and Links:

1. A lecture on currency arbitrage A link to a youtube video.

1.5 Mathematical Modeling

Rating

Student: contains scenes of mild algebra or calculus that may require guid-

ance.

Section Starter Question

Do you believe in the ideal gas law? Does it make sense to “believe in” an

equation? What do we really mean when we say we “believe in” an equation?

Key Concepts

1. All mathematical models are wrong, but some mathematical models
   are useful.


2. If the modeling assumptions are satisfied, proper mathematical models
   should predict well given a wide range of conditions corresponding to
   the assumptions.


3. When observed outcomes deviate from predicted ideal behavior in hon-
   est scientific or engineering work, then we must then alter our assump-
   tions, re-derive the quantitative relationships, perhaps with more so-
   phisticated mathematics or introducing more quantities and begin the

1.4 The cycle of modeling

Vocabulary

1. Amathematical modelis a mathematical structure (often an equa-
   tion) expressing a relationship among a limited number of quantifiable
   elements from the “real world” or some isolated portion of it.